Issues modelling particle spin

Hello, I've been working on my code to simulate particles diffusing in a 1D box in the presence of a magnetic field gradient. The gradient is in one dimension but increases in strength as a function of position in the box.

The issue arises with the summing of the spins, they should all theoretically become out of phase and sum to 0, but they usually generate large numbers. Can anyone see any issues with the code or, even worse, my physics!

Code:

clear all
h = 1000000; 
T = 1*10^-6; 
ts = 10^-7; 
D = 0.282;
ga = (267.513 * 10^6)*360/(2*pi);
xsi=(2*D*ts)^0.5;
W = xsi*25;
B0 = 0.00001;
G = 20;
t = ts;
m = 1;
omg = pi*ones(1,h);
n = zeros(1,h);
rot = zeros(1,h);
r = ones(1,h);
k = 1;
bins = (-W:xsi:W);

while sum(rot) >= 0;
    x = round(rand(1,h));
    for m = 1 : h;
        if n(m) >= W - xsi
            n(m) = n(m) - xsi;
        elseif n(m) <= - W + xsi
            n (m) = n(m) + xsi;
        else
            if x(m) == 1
               n(m) = n(m) + xsi;
            elseif x(m) == 0
               n(m) = n(m) - xsi;
            end
        end
        omg(m) = ga*(G*n(m)+B0)*ts;
        rot(m) = rot(m) + omg(m);
    end

      t = t + ts;
      k = k + 1;
  end

sum(rot)